Please, thank SteveC who was the mind behind the idea!
Don'worry, as long as it is smaller in diameter than the pin (but having a larger/thicker one reduces the number of divots and improves appearances), it should be alright. Here are some of my "fixed" ones; although difficult to see, you'll find divots going around the pivots' perimeter and my "tool of choice" for doing such work. I use the anvil end of a 4" bench vise as base.
Hope it for you in the end.